Partial wave expansion and Wightman positivity in conformal field theory

Abstract

A new method for computing exact conformal partial wave expansions is developed and applied to approach the problem of Hilbert space (Wightman) positivity in a non-perturbative four-dimensional quantum field theory model. The model is based on the assumption of global conformal invariance on compactified Minkowski space. Bilocal fields arising in the harmonic decomposition of the operator product expansion prove to be a powerful instrument in exploring the field content. In particular, in the theory of a field of dimension 4 which has the properties of a (gauge invariant) Lagrangian, the scalar field contribution to the 6-point function of the twist 2 bilocal field is analyzed with the aim to separate the free field part from the nontrivial part.

26 pages. v2: references and comments added, numerical errors corrected

References in corpus (2)

• Vertex Algebras in Higher Dimensions and Globally Conformal Invariant Quantum Field Theory
• Globally conformal invariant gauge field theory with rational correlation functions

Cited by in corpus (6)

• Harmonic bilocal fields generated by globally conformal invariant scalar fields
• Jacobi Identity for Vertex Algebras in Higher Dimensions
• Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields
• Quantum field theory in terms of consistency conditions I: General framework, and perturbation theory via Hochschild cohomology
• Infinite dimensional Lie algebras in 4D conformal quantum field theory
• On invariants and scalar chiral correlation functions in N=1 superconformal field theories